Scope and Sequence 2009-2010 TEXARKANA INDEPENDENT SCHOOL DISTRICT I = Introduced P = Practiced M= Mastered 111.23 Mathematics, Grading Period Grade 7. Middle School 1 2 3 4 5 6 (1) The student represents and uses numbers in a variety of equivalent forms. The student is expected to: (A) compare and order integers and positive rational numbers •Using multiple forms of positive rational numbers, including I P P P M numbers represented as fractions, percents, decimals, positive and negative integers within a single problem. (B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator I P P P M Including mixed numbers (C) represent squares and square roots using geometric models I P P M (2) The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to: (A) represent multiplication and division situations involving fractions and decimals with models, including concrete objects, I P P P M pictures, words, and numbers Including writing or selecting the correct expression (B) use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals I P P P M Examples include: Problems where your answer choices are models (C) use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and I P P P M connect the actions to algorithms (D) use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student- teacher ratio I P P M Including: •Fractions and decimals •Cross multiply and solve for x (E) simplify numerical expressions involving order of operations and exponents I P P P M Including negative values (F) select and use appropriate operations to solve problems and justify the selections Examples include: IP P P P M •Problems with multiple operations •Problems with answer grids (G) determine the reasonableness of a solution to a problem Including problems with the appropriate range IP P P P M (3) The student solves problems involving direct proportional relationships. The student is expected to: (A) estimate and find solutions to application problems involving percent Including: I P M •Percent increase •Percent decrease (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units Including: I P P M •Setting up a proportion problem from word problems •Using data in a table •Measurements using standard and metric units •Unit conversions (4) The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving unit conversions, perimeter, area, circumference, volume, and scaling Including: •Perimeter of regular polygons •Circumference •Area of squares, rectangles, triangles, circles, trapezoids IP PM •Volume of rectangular prism, cylinders, cubes •Conversion from one standard unit to another as listed on the formula chart •Conversion from one metric unit to another as listed on the formula chart (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling Including: •Vocabulary (i.e. independent and dependent variable) •Data that models a linear relationship. Example: Perimeter IP M and conversions •Data that models a quadratic (second degree) relationship. Example: Area •Data that models a third degree relationship. Example: Volume (C) use words and symbols to describe the relationship between the terms in an arithmetic sequence (with a constant rate of change) and their positions in the sequence Including: I P P M •The nth term table •Finding the nth term •Using nth term to find a specific term (5) The student uses equations to solve problems. The student is expected to: (A) use concrete and pictorial models to solve equations and use symbols to record the actions I P P P M Including equations with two variables (B) formulate problem situations when given a simple equation and formulate an equation when given a problem situation Including prerequisites of: •Translating word phrases to algebraic expressions I P P P M •Translating word phrases to algebraic equations. Including focusing on operational vocabulary (Examples: difference, total, product, and quotient) (6) The student compares and classifies two- and three- dimensional figures using geometric vocabulary and properties. The student is expected to: (A) use angle measurements to classify pairs of angles as complementary or supplementary Including: IP P M •Diagrams with multiple angles •Prerequisite: name angles with three points (B) use properties to classify triangles and quadrilaterals Including: •Triangle vocabulary: (i.e. acute, obtuse, right (define legs and IP PM M hypotenuse), equiangular, isosceles, equilateral, and scalene) •Quadrilateral terms: (i.e. parallelogram, rectangle, square, trapezoid, and rhombus) (C) use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders IP PM Including vocabulary (i.e. faces, edges, vertices, bases, and lateral face) (D) use critical attributes to define similarity Include: All polygons Corresponding sides are proportional I P P M Corresponding angles are congruent Using proportions to find missing sides Identifying pictorially similar figures •Students needing to identify corresponding angles and sides by a similarity statement. Example: ∆ABC similar ~ ∆DEF (7) The student uses coordinate geometry to describe location on a plane. The student is expected to: (A) locate and name points on a coordinate plane using ordered pairs of integers Include: IP P M •All four quadrants •Vocabulary: (i.e. x-axis, x-coordinate, y-coordinate, quadrants, origin) (B) graph reflections across the horizontal or vertical axis and graph translations on a coordinate plane Include all four quadrants I P M •Reflection across x-axis (x,y) → (x,-y) •Reflection across y-axis (x,y) → (-x,y) (8) The student uses geometry to model and describe the physical world. The student is expected to: (A) sketch three-dimensional figures when given the top, side, and IP PM front views (B) make a net (two-dimensional model) of the surface area of a three-dimensional figure Include figures such as: •Cylinders IP PM •Cones •Prisms •Pyramids •Cube (C) use geometric concepts and properties to solve problems in fields such as art and architecture Include all two- and three-dimensional figures listed on the IP PM formula chart and combinations of figures such as a half circle and rectangle pieced together. (9) The student solves application problems involving estimation and measurement. The student is expected to: (A) estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes Include: IP PM •All polygons on the formula chart •Using rulers on formula chart •Problems with answer grids (B) connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders IP PM Including matching nets and models to appropriate formulas to problem solve. (C) estimate measurements and solve application problems IP PM involving volume of prisms (rectangular and triangular) and cylinders (10) The student recognizes that a physical or mathematical model can be used to describe the experimental and theoretical probability of real-life events. The student is expected to: (A) construct sample spaces for simple or composite experiments Including with and without replacement. IPM Construct tree diagrams (B) find the probability of independent events Including: •Flipping a coin •Drawing an object from a box without looking IPM •Compound events: Drawing an object from a box without looking, replacing the object, and drawing another object (and/or situations) (11) The student understands that the way a set of data is displayed influences its interpretation. The student is expected to: (A) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection I PM Including: •Frequency tables •Vocabulary (i.e. intervals, scale) (B) make inferences and convincing arguments based on an analysis of given or collected data I PM Including using the data to make predictions. (12) The student uses measures of central tendency and range to describe a set of data. The student is expected to: (A) describe a set of data using mean, median, mode, and range P M (B) choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation Including problems such as: I PM Given a set of data the student selects the “best” measure of central tendency to describe that data (13) The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics IP P P P PM This student expectation can be tested in every strand including one or more than one TEKS at a time. (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness IP P P P PM This student expectation can be tested in every strand including one or more than one TEKS at a time. (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working IP P P P PM backwards to solve a problem This student expectation can be tested in every strand including one or more than one TEKS at a time. (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, I P P P PM and number sense to solve problems (14) The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models I P P P PM This student expectation can be tested in every strand including one or more than one TEKS at a time. (B) evaluate the effectiveness of different representations to I PM communicate ideas (15) The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and non- examples Including: •Defining a concept introduced at a higher grade IP P P M •Showing a pattern, examples, and/or non-examples •Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples (B) validate his/her conclusions using mathematical properties and relationships I P P P M This student expectation can be tested in every strand including one or more than one TEKS at a time.
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